A genuine belief serves a functional purpose, rooted in our survival instinct, evident even in dreams. Consider the act of climbing Mount Everest, whether awake or dreaming: the belief that incorrectly tying a prussic knot will lead to a fatal fall is genuine, even if ultimately false. The knot's actual correctness is secondary; the belief's genuineness stems from its functionality, providing emotional composure to confidently proceed, associating the action with survival. This belief cannot be fictional, or panic would ensue, as if in a dream.
Dreams, in this context, are fictions, while awake states are not. Panic is more likely in a dream than while fully awake. This extends to modern industrial processes, which could be likened to a dream. However, even in a dream, operating heavy machinery necessitates a genuine belief in its safe operation, otherwise the dreamer would awaken in fear due to lack of confidence in their survival.
Recreational activities also relate to social survival, like winning or avoiding defeat in billiards, or conforming to religious practices to avoid ostracism. Yet, genuine belief becomes less certain when infinity enters the equation. Choosing the next best move based on number theory is a "genuine fiction," as infinity cannot be truly understood in the same way as tying a prussic knot or kneeling in church. We cannot genuinely believe we know infinity, as our confidence in it is not comparable to that in practical skills.
Belief in an infinity might merely be a step towards another infinity. While we might genuinely believe we know the infinity of prime numbers, this seems fictional given its relativity to decimal places between primes or an even more perplexing infinity. Thus, genuine belief in the face of various infinities cannot be as genuine as beliefs about religious practices within a community. This suggests that genuine belief has both a qualitative interpersonal aspect and a rational abstract component, which deconstructs when quantitative numerical methodology introduces contradictions imposed by infinity on qualitative sentiments based on perception.